The study of neural network-based controller for controlling dissolved oxygen concentration in a sequencing batch reactor

The design and development of the neural network (NN)-based controller performance for the activated sludge process in sequencing batch reactor (SBR) is presented in this paper. Here we give a comparative study of various neural network (NN)-based controllers such as the direct inverse control, internal model control (IMC) and hybrid NN control strategies to maintain the dissolved oxygen (DO) level of an activated sludge system by manipulating the air flow rate. The NN inverse model-based controller with the model-based scheme represents the controller, which relies solely upon the simple NN inverse model. In the IMC, both the forward and inverse models are used directly as elements within the feedback loop. The hybrid NN control consists of a basic NN controller in parallel with a proportional integral (PI) controller. Various simulation tests involving multiple set-point changes, disturbances rejection and noise effects were performed to review the performances of these various controllers. From the results it can be seen that hybrid controller gives the best results in tracking set-point changes under disturbances and noise effects.     

Controlling the dynamical behavior of a circle map model of the human heart

One-dimensional circle maps are good models for describing the nonlinear dynamical behavior of two interacting oscillators. They have been employed to characterize the interaction between a periodic external forcing stimulus and an in vitro preparation of chick embryonic cardiac cells. They have also been used to model some human cardiac arrythmias such as modulated ventricular parasystole. In this paper, we describe several techniques involving engineering feedback control theory applied to a circle map model of human heart parasystole. Through simulations of the mathematical model, we demonstrate that a desired target phase relationship between the normal sinus rhythm and an abnormal ectopic pacemaker can be achieved rapidly with low-level external stimulation applied to the system. Specifically, we elucidate the linear, self-tuning, and nonlinear feedback approaches to control. The nonlinear methods are the fastest and most accurate, yet the most complex and computationally expensive to implement of the three types. The linear approach is the easiest to implement but may not be accurate enough in real applications, and the self-tuning methods are a compromise between the other two. The latter was successful in tracking a variety of period-1, period-2, and period-3 target phase trajectories of the heart model.     

Nonlinear modelling of renal vasoaction

The control of blood pressure is a complex mixture of neural, hormonal and intrinsic interactions at the level of the heart, kidney and blood vessels. While experimental approaches to understanding these interactions are useful, it remains difficult to conduct experiments to quantify these interactions as the number of parameters increases. Thus, modelling of such physiological systems can offer considerable assistance. Typical mathematical models which describe the ability of the blood vessels to change their diameter (vasoconstriction) assume linearity of operation. However, due to the interaction of multiple vasocontrictive and vasodilative effectors, there is a significant nonlinear response to the influence of neural factors, particularly at higher levels of nerve activity (often seen in subjects with high blood pressure) which leads to low blood flow rates. This paper proposes a number of nonlinear mathematical models for the relationship between neural influences (sympathetic nerve activity (SNA)) and renal blood flow, using a feedback path to model the predominantly nonlinear effect of local vasoactive modulators such as nitric oxide, which oppose the action of SNA. The model structures are motivated by basic physiological principles, while the model parameters are determined using numerical optimisation techniques using open-loop data collected from rabbits. The models were verified by demonstrating correlation between experimental results and model outputs.     

Controlling the dynamical behavior of a circle map model of the human heart

One-dimensional circle maps are good models for describing the nonlinear dynamical behavior of two interacting oscillators. They have been employed to characterize the interaction between a periodic external forcing stimulus and an in vitro preparation of chick embryonic cardiac cells. They have also been used to model some human cardiac arrythmias such as modulated ventricular parasystole. In this paper, we describe several techniques involving engineering feedback control theory applied to a circle map model of human heart parasystole. Through simulations of the mathematical model, we demonstrate that a desired target phase relationship between the normal sinus rhythm and an abnormal ectopic pacemaker can be achieved rapidly with low-level external stimulation applied to the system. Specifically, we elucidate the linear, self-tuning, and nonlinear feedback approaches to control. The nonlinear methods are the fastest and most accurate, yet the most complex and computationally expensive to implement of the three types. The linear approach is the easiest to implement but may not be accurate enough in real applications, and the self-tuning methods are a compromise between the other two. The latter was successful in tracking a variety of period-1, period-2, and period-3 target phase trajectories of the heart model.     

Mass and Information Feedbacks through Receptor Endocytosis Govern Insulin Signaling as Revealed Using a Parameter-free Modeling Framework

Insulin and other hormones control target cells through a network of signal-mediating molecules. Such networks are extremely complex due to multiple feedback loops in combination with redundancy, shared signal mediators, and cross-talk between signal pathways. We present a novel framework that integrates experimental work and mathematical modeling to quantitatively characterize the role and relation between co-existing submechanisms in complex signaling networks. The approach is independent of knowing or uniquely estimating model parameters because it only relies on (i) rejections and (ii) core predictions (uniquely identified properties in unidentifiable models). The power of our approach is demonstrated through numerous iterations between experiments, model-based data analyses, and theoretical predictions to characterize the relative role of co-existing feedbacks governing insulin signaling. We examined phosphorylation of the insulin receptor and insulin receptor substrate-1 and endocytosis of the receptor in response to various different experimental perturbations in primary human adipocytes. The analysis revealed that receptor endocytosis is necessary for two identified feedback mechanisms involving mass and information transfer, respectively. Experimental findings indicate that interfering with the feedback may substantially increase overall signaling strength, suggesting novel therapeutic targets for insulin resistance and type 2 diabetes. Because the central observations are present in other signaling networks, our results may indicate a general mechanism in hormonal control.     

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.     

A Model of Postural Control in Quiet Standing: Robust Compensation of Delay-Induced Instability Using Intermittent Activation of Feedback Control

The main purpose of this study is to compare two different feedback controllers for the stabilization of quiet standing in humans, taking into account that the intrinsic ankle stiffness is insufficient and that there is a large delay inducing instability in the feedback loop: 1) a standard linear, continuous-time PD controller and 2) an intermittent PD controller characterized by a switching function defined in the phase plane, with or without a dead zone around the nominal equilibrium state. The stability analysis of the first controller is carried out by using the standard tools of linear control systems, whereas the analysis of the intermittent controllers is based on the use of Poincaré maps defined in the phase plane. When the PD-control is off, the dynamics of the system is characterized by a saddle-like equilibrium, with a stable and an unstable manifold. The switching function of the intermittent controller is implemented in such a way that PD-control is ‘off’ when the state vector is near the stable manifold of the saddle and is ‘on’ otherwise. A theoretical analysis and a related simulation study show that the intermittent control model is much more robust than the standard model because the size of the region in the parameter space of the feedback control gains (P vs. D) that characterizes stable behavior is much larger in the latter case than in the former one. Moreover, the intermittent controller can use feedback parameters that are much smaller than the standard model. Typical sway patterns generated by the intermittent controller are the result of an alternation between slow motion along the stable manifold of the saddle, when the PD-control is off, and spiral motion away from the upright equilibrium determined by the activation of the PD-control with low feedback gains. Remarkably, overall dynamic stability can be achieved by combining in a smart way two unstable regimes: a saddle and an unstable spiral. The intermittent controller exploits the stabilizing effect of one part of the saddle, letting the system evolve by alone when it slides on or near the stable manifold; when the state vector enters the strongly unstable part of the saddle it switches on a mild feedback which is not supposed to impose a strict stable regime but rather to mitigate the impending fall. The presence of a dead zone in the intermittent controller does not alter the stability properties but improves the similarity with biological sway patterns. The two types of controllers are also compared in the frequency domain by considering the power spectral density (PSD) of the sway sequences generated by the models with additive noise. Different from the standard continuous model, whose PSD function is similar to an over-damped second order system without a resonance, the intermittent control model is capable to exhibit the two power law scaling regimes that are typical of physiological sway movements in humans.     

UKF-based closed loop iterative learning control of epileptiform wave in a neural mass model

A novel closed loop control framework is proposed to inhibit epileptiform wave in a neural mass model by external electric field, where the unscented Kalman filter method is used to reconstruct dynamics and estimate unmeasurable parameters of the model. Specifically speaking, the iterative learning control algorithm is introduced into the framework to optimize the control signal. In the proposed method, the control effect can be significantly improved based on the observation of the past attempts. Accordingly, the proposed method can effectively suppress the epileptiform wave as well as showing robustness to noises and uncertainties. Lastly, the simulation is carried out to illustrate the feasibility of the proposed method. Besides, this work shows potential value to design model-based feedback controllers for epilepsy treatment.     

Full-state tracking control of a mobile robot using neural networks

In this paper a nonholonomic mobile robot with completely unknown dynamics is discussed. A mathematical model has been considered and an efficient neural network is developed, which ensures guaranteed tracking performance leading to stability of the system. The neural network assumes a single layer structure, by taking advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot dynamic parameters. No assumptions relating to the boundedness is placed on the unmodeled disturbances. It is capable of generating real-time smooth and continuous velocity control signals that drive the mobile robot to follow the desired trajectories. The proposed approach resolves speed jump problem existing in some previous tracking controllers. Further, this neural network does not require offline training procedures. Lyapunov theory has been used to prove system stability. The practicality and effectiveness of the proposed tracking controller are demonstrated by simulation and comparison results.     

Optimization and evaluation of a proportional derivative controller for planar arm movement

In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.     

Output regulation of a class of unstructured models of continuous bioreactors: steady-state approaches

This article deals with the output regulation of continuous bioreactors in the face of constant disturbances and inverse dynamics. Nonlinear controllers developed on the basis of approximate equilibrium manifolds can almost attenuate measurable or unmeasurable disturbances on the output. This nonlinear feed-forward/feedback control framework without any tuning parameters can be directly implemented to strictly nonlinear systems. Under dynamic actuator constraints and the availability of only output signals for use in the control law, closed-loop simulations demonstrate that the proposed control techniques are superior to a nonlinear PI control scheme based on the identified Hammerstein model.     

Adaptive fuzzy control with output feedback for H infinity tracking of SISO nonlinear systems

Observer-based adaptive fuzzy H(infinity) control is proposed to achieve H(infinity) tracking performance for a class of nonlinear systems, which are subject to model uncertainty and external disturbances and in which only a measurement of the output is available. The key ideas in the design of the proposed controller are (i) to transform the nonlinear control problem into a regulation problem through suitable output feedback, (ii) to design a state observer for the estimation of the non-measurable elements of the system's state vector, (iii) to design neuro-fuzzy approximators that receive as inputs the parameters of the reconstructed state vector and give as output an estimation of the system's unknown dynamics, (iv) to use an H(infinity) control term for the compensation of external disturbances and modelling errors, (v) to use Lyapunov stability analysis in order to find the learning law for the neuro-fuzzy approximators, and a supervisory control term for disturbance and modelling error rejection. The control scheme is tested in the cart-pole balancing problem and in a DC-motor model.     

Pattern formation of Rho GTPases in single cell wound healing

The Rho GTPases—Rho, Rac, and Cdc42—control an enormous variety of processes, many of which reflect activation of these GTPases in spatially confined and mutually exclusive zones. By using mathematical models and experimental results to establish model parameters, we analyze the formation and segregation of Rho and Cdc42 zones during Xenopus oocyte wound repair and the role played by Abr, a dual guanine nucleotide exchange factor–GTPase-activating protein, in this process. The Rho and Cdc42 zones are found to be best represented as manifestations of spatially modulated bistability, and local positive feedback between Abr and Rho can account for the maintenance and dynamic properties of the Rho zone. In contrast, the invocation of an Abr-independent positive feedback loop is required to account for Cdc42 spatial bistability. In addition, the model replicates the results of previous in vivo experiments in which Abr activity is manipulated. Further, simulating the model with two closely spaced wounds made nonintuitive predictions about the Rho and Cdc42 patterns; these predictions were confirmed by experiment. We conclude that the model is a useful tool for analysis of Rho GTPase signaling and that the Rho GTPases can be fruitfully considered as components of intracellular pattern formation systems.     

Motion control of musculoskeletal systems with redundancy

Motion control of musculoskeletal systems for functional electrical stimulation (FES) is a challenging problem due to the inherent complexity of the systems. These include being highly nonlinear, strongly coupled, time-varying, time-delayed, and redundant. The redundancy in particular makes it difficult to find an inverse model of the system for control purposes. We have developed a control system for multiple input multiple output (MIMO) redundant musculoskeletal systems with little prior information. The proposed method separates the steady-state properties from the dynamic properties. The dynamic control uses a steady-state inverse model and is implemented with both a PID controller for disturbance rejection and an artificial neural network (ANN) feedforward controller for fast trajectory tracking. A mechanism to control the sum of the muscle excitation levels is also included. To test the performance of the proposed control system, a two degree of freedom ankle–subtalar joint model with eight muscles was used. The simulation results show that separation of steady-state and dynamic control allow small output tracking errors for different reference trajectories such as pseudo-step, sinusoidal and filtered random signals. The proposed control method also demonstrated robustness against system parameter and controller parameter variations. A possible application of this control algorithm is FES control using multiple contact cuff electrodes where mathematical modeling is not feasible and the redundancy makes the control of dynamic movement difficult.     

Computational model predicts paracrine and intracellular drivers of fibroblast phenotype after myocardial infarction

The fibroblast is a key mediator of wound healing in the heart and other organs, yet how it integrates multiple time-dependent paracrine signals to control extracellular matrix synthesis has been difficult to study in vivo. Here, we extended a computational model to simulate the dynamics of fibroblast signaling and fibrosis after myocardial infarction (MI) in response to time-dependent data for nine paracrine stimuli. This computational model was validated against dynamic collagen expression and collagen area fraction data from post-infarction rat hearts. The model predicted that while many features of the fibroblast phenotype at inflammatory or maturation phases of healing could be recapitulated by single static paracrine stimuli (interleukin-1 and angiotensin-II, respectively), mimicking the reparative phase required paired stimuli (e.g. TGFβ and endothelin-1). Virtual overexpression screens simulated with either static cytokine pairs or post-MI paracrine dynamic predicted phase-specific regulators of collagen expression. Several regulators increased (Smad3) or decreased (Smad7, protein kinase G) collagen expression specifically in the reparative phase. NADPH oxidase (NOX) overexpression sustained collagen expression from reparative to maturation phases, driven by TGFβ and endothelin positive feedback loops. Interleukin-1 overexpression had mixed effects, both enhancing collagen via the TGFβ positive feedback loop and suppressing collagen via NFκB and BAMBI (BMP and activin membrane-bound inhibitor) incoherent feed-forward loops. These model-based predictions reveal network mechanisms by which the dynamics of paracrine stimuli and interacting signaling pathways drive the progression of fibroblast phenotypes and fibrosis after myocardial infarction.     

A mathematical model of the adaptive control of human arm motions

This paper discusses similarities between models of adaptive motor control suggested by recent experiments with human and animal subjects, and the structure of a new control law derived mathematically from nonlinear stability theory. In both models, the control actions required to track a specified trajectory are adaptively assembled from a large collection of simple computational elements. By adaptively recombining these elements, the controllers develop complex internal models which are used to compensate for the effects of externally imposed forces or changes in the physical properties of the system. On a motor learning task involving planar, multi-joint arm motions, the simulated performance of the mathematical model is shown to be qualitatively similar to observed human performance, suggesting that the model captures some of the interesting features of the dynamics of low-level motor adaptation. Received: 20 September 1994 / Accepted in revised form: 18 November 1998